Premium
On the L p error of the Grenander‐type estimator in the Cox model
Author(s) -
Durot Cécile,
Musta Eni
Publication year - 2020
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12218
Subject(s) - estimator , mathematics , monotone polygon , statistics , weibull distribution , minimax estimator , proportional hazards model , efficient estimator , type (biology) , parametric statistics , minimum variance unbiased estimator , ecology , geometry , biology
We consider the Cox regression model and study the asymptotic global behavior of the Grenander‐type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for L p ‐error of the Grenander‐type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the L p ‐distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.